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Stability and branching of stationary rotations in a planar problem of motion of mutually gravitating triangle and material point. (Russian. English summary) Zbl 1371.70053
Summary: The planar motion of an equilateral triangle with equal masses at vertices and of a point subjected to mutual Newtonian attraction is considered. Necessary conditions for the stability of “straight”, axial steady configurations, when the massive point is located on one of the symmetry axes of the triangle, are studied. The generation of other, “oblique”, steady configurations is discussed in connection with the variation, for certain parameter values, of the degree of instability of some “straight” steady configurations.

70K20 Stability for nonlinear problems in mechanics
70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
70F05 Two-body problems
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